An experimental fireworks shell is launched vertically from point A with an init

Question

An experimental fireworks shell is launched vertically from point A with an initial velocity of magnitude v0 = 112 ft/sec. In addition to the acceleration due to gravity, an internal thrusting mechanism causes a constant acceleration component of 1.8g in the direction shown for the first 1.9 seconds of flight, after which the thruster ceases to function. Determine the maximum height h achieved, the total flight time t, the net horizontal displacement x from point A, and plot the entire trajectory. Neglect any acceleration due to aerodynamics.

Explanation / Answer

so vertical component of acceleration for 1.9 s 1.8g* sin 59 -g = 17.467 ft/s^2 horizonntal component g*cos 59 = 16.57 ft/s^2 After 1.9 sec ; x = 0.5*16.57*1.9^2 = 29.90885 ft vx =16.57*1.9 =31.483 ft/s y = 112*1.9+0.5*17.467*1.9^2 = 244.3279 ft vy= 112 + 17.467*1.9 = 145.1873 ft/s now 145.1873^2 =2*32.174*h h= 327.586 ft so maximum height = h+y = 571.9115 ft 145.1873/32.174 = t t= 4.5125 s so total time = t+1.9 = 6.4125 s Horizontal displacement = 29.90885 + 31.483*4.5125 = 171.98 ft

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